# Warped space

Hi

I'm not sure if Einstein's idea of warped space can be adequately described without math, but from the explanation in many general consumption texts: If space warps in response to a gravitational force, doesn't that imply that space has mass?

If so, wouldn't the gravitational constant combined with gravitational lensing give some idea how much mass/energy space possessed?

Ken

## Answers and Replies

If space warps in response to a gravitational force, doesn't that imply that space has mass?

You're confusing yourself a bit here. The warping of space time IS, in a sense, the gravitational force. Mass tells space time how to curve, space time curvature tells mass how to move.

You're confusing yourself a bit here. The warping of space time IS, in a sense, the gravitational force. Mass tells space time how to curve, space time curvature tells mass how to move.

I guess the question is: What exactly is warping? Space isn't really anything other than the separation between objects so how exactly do you warp a separation?

Unwarped space - for 2 points (x1, y1) and (x2,y2)

$$distance^2 = ( x_1 - x_2)^2 + (y_1 - y_2)^2$$

warped space -

$$distance^2 = a^2 ( x_1 - x_2)^2 + b^2(y_1 - y_2)^2$$

If a and b depend on the coordinates, that's one way to warp a separation.

warped space -

$$distance^2 = a^2 ( x_1 - x_2)^2 + b^2(y_1 - y_2)^2$$

If a and b depend on the coordinates, that's one way to warp a separation.

How would the dependence of a,b on the coordinates manifest itself? As functions of x,y not just arbitrary selections?

I'm a sculptor by training so my only exposure to (and understanding of) warped space is the "rubber sheet" idea. Since gravity isn't a directional phenomenon and attracts with equal strength in all directions (is that right?) the warping in 3 dimensions around gravitational objects would be more like a thickening. Sort of an onion where inner layers are "denser" or more closely spaced than outer layers. If that's correct then space wouldn't really be "curved" around gravitational objects but "thickened" wouldn't it?

If that onion description hasn't left the ballpark entirely, then gravitational lensing would be caused by an increased refractive index due to "thicker" or "denser" space rather than curvature.

And just running with this (perhaps incorrect) idea, it would follow that space itself refracts light to greater or lesser degrees depending on its proximity to gravitational bodies.

I'm sure I've left the ballpark at this point so will stop there : )

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Ktoz,
in gravitational theories, the numbers a and b would be components of
the field metric, viz the components of the field itself. In a 4-D universe,
there are 10 such numbers.

Your analogy of space thickening is accurate. The thicker it is the more bent it is ( like some people). Except it could be space-time that is thickening. Yes, light is refracted in a gravitational field. In a sense, the paths of light beams defines the space ( arty, or what ?).
M

In gravitational theories, the numbers a and b would be components of the field metric, viz the components of the field itself. In a 4-D universe, there are 10 such numbers.

Thanks. I'll have to read up on fields to appreciate this more fully.

Your analogy of space thickening is accurate. The thicker it is the more bent it is ( like some people). Except it could be space-time that is thickening. Yes, light is refracted in a gravitational field. In a sense, the paths of light beams defines the space ( arty, or what ?).
M

After chewing on this some more, I think the thickening/refracting concept breaks down because it implies that, for light, there is effectively "more" space per unit distance.

Given physical explanations for refraction (change in speed with a change in medium) light should slow down near gravitating bodies which is the exact opposite of what happens to masses near gravitating bodies. This would lead (I think) to the odd result that as a mass approaches an area of "thickened" space, it accelerates where as light approaches an area of "thickened" space it decelerates.

This implies that there exists some curvature/thickening threshold of space at which matter and light naturally travel at the same speed. I don't have the math skills to calculate this threshold but, if curvature/thickening is true, then it should exist.

In the extreme case of a black hole, (assuming they are truly singularities) this would mean that, if a mass could somehow survive the trip, it would pass from one side of a black hole to the other in zero time while it would take light an infinite amount of time to cover the same distance.

I'm sure I'm WAY out in the weeds now but fun concepts to let your imagination run around in. :)

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ranger
Gold Member
Given physical explanations for refraction (change in speed with a change in medium) light should slow down near gravitating bodies which is the exact opposite of what happens to masses near gravitating bodies. This would lead (I think) to the odd result that as a mass approaches an area of "thickened" space, it accelerates where as light approaches an area of "thickened" space it decelerates.
You should read up on Gravitational redshifting.
In the extreme case of a black hole, (assuming they are truly singularities) this would mean that, if a mass could somehow survive the trip, it would pass from one side of a black hole to the other in zero time while it would take light an infinite amount of time to cover the same distance.
How did you arrive at this conclusion? A photon doesnt "see" time, or space.

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You should read up on Gravitational redshifting.

How did you arrive at this conclusion? A photon doesnt "see" time, or space.

I'm going to switch terms here from "thickened" or "curved" space to "squeezed" space as that seems to more intuitively describe the effect in 3 dimensions.

I was using a conventional model of refraction, where light slows upon entering a denser material. Since squeezed space seems to produce an effect indistinguishable from refraction (at least with my layman's understanding of the concepts) it would seem to follow that as the squeezing of space approaches infinity, as in a black hole, the time delay observed in gravitational lensing is, for all intents, indistinguishable from an increase in distance. For light, a black hole could be described as an infinitely wide bubble in normal spacetime. It's just a different perspective.

Back into the weeds...

Matter experiences squeezed space as an acceleration or decrease in distance so as mentioned before, there should be a squeezing threshold at which matter and light approach a gravitational body at the same speed. Beyond this threshold, matter would move faster than light in it's immediate vicinity. (but not faster than C)

Added later:
Reading up on force carriers, it would appear that molecules and atoms would fragment at the squeezing threshold as the electromagnetic force carriers (photons) would move slower than the particles themselves. Atomic nuclei could still exist though provided the squeezing was not too extreme. This state seems strikingly similar to the state of matter inside stars, a roiling soup of free photons and atomic particles.

Very deep in the weeds now... The warped space musings of a warped art mind :)

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